Singular, hypersingular and singular free electromagnetic fields at wedge tips in metamaterials

The engineering response of metamaterials has a dramatic impact on the physics, optics and engineering communities, because they offer electromagnetic properties that are difficult or impossible to achieve with conventional materials. In this paper, an asymptotic analysis of the electromagnetic fields at multi-material wedges composed of metamaterials is proposed. This is made possible by removing the assumption of positive electric permittivities and magnetic permeabilities, an hypothesis which usually applies to conventional materials. Exploring the whole range of variability of these electromagnetic properties, it is shown that, in addition to the classical real eigenvalues 0 ⩽ λ < 1 leading to power-law singularities of the type O(rλ−1) as r → 0, it is also possible to find imaginary eigenvalues leading to hypersingular solutions, as well as nonsingular configurations for a suitable choice of the negative electric permittivities and magnetic permeabilities of the media. Moreover, to fully characterize the asymptotic fields, the analysis is not only restricted to the determination of the lowest real and complex eigenvalues, but is also extended to the evaluation of the higher-order nonsingular ones. The obtained analytical results collected in synthetic diagrams are expected to have impact on the design of micro- and nano-electro-mechanical systems.